Let f(x,y) = 24xy for 0 <151,0 Sys1,0

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Let F X Y 24xy For 0 151 0 Sys1 0 X Y 1 And S X Y 0 Otherwise Part A Show That F X Y Is A Joint Probability 1 (29.15 KiB) Viewed 107 times

Let f(x,y) = 24xy for 0 <151,0 Sys1,0 <x+y< 1 and S(x,y) = 0 otherwise. part a) Show that f(x,y) is a joint probability density function. part b) Find E{X}. part c) Find E{Y}. part d) Find Var[X] and Var[Y]. part e) Now obtain the density of the random variable T = X + Y. part 1) Compute the expected value and variance of T. part g) As T=X+ Y you can address the following two questions: Is E[X + Y) = E[X] + E[Y]? Is Var[X + Y) = Var[X] + Var[Y]?